Final answer:
To list the sides of triangle FGH in order from least to greatest, we need to find the measures of the angles F, G, and H in terms of x. Given that m∠F = 5x + 6, m∠G = 12x – 4, and m∠H = 4x + 31, we can solve for x and then substitute it into expressions for each side to determine their values.
Step-by-step explanation:
To list the sides of triangle FGH in order from least to greatest, we need to find the measures of the angles F, G, and H in terms of x. Given that m∠F = 5x + 6, m∠G = 12x – 4, and m∠H = 4x + 31, we can solve for x. Once we have the values of x, we can substitute them into the expressions for each side length to determine their values. Then, we can list the sides in order from least to greatest.
Let's solve for x first:
m∠F = 5x + 6
m∠G = 12x – 4
m∠H = 4x + 31
The sum of the angles in a triangle is 180 degrees, so:
m∠F + m∠G + m∠H = 180
Substituting the given angle measures:
(5x + 6) + (12x – 4) + (4x + 31) = 180
Combine like terms:
21x + 33 = 180
Subtract 33 from both sides:
21x = 147
Divide both sides by 21:
x = 7
Now that we have the value of x, we can substitute it into the expressions for each side length:
Side FG: 3x
Side GH: x + 5
Side FH: 2x + 6
Substituting x=7:
Side FG = 3(7) = 21
Side GH = 7 + 5 = 12
Side FH = 2(7) + 6 = 20
Listed in order from least to greatest: Side GH, Side FH, Side FG